An Exact Connection between two Solvable SDEs and a Nonlinear Utility Stochastic PDE

Motivated by the work of Musiela and Zariphopoulou \cite{zar-03}, we study the It\^o random fields which are utility functions $U(t,x)$ for any $(\omega,t)$. The main tool is the marginal utility $U_x(t,x)$ and its inverse expressed as the opposite of the derivative of the Fenchel conjuguate \tU(t,y). Under regularity assumptions, we associate a $SDE(\mu, \sigma)$ and its adjoint SPDE$(\mu, \sigma)$ in divergence form whose $U_x(t,x)$ and its inverse -\tU_y(t,y) are monotonic solutions. More generally, special attention is paid to rigorous justification of the dynamics of inverse flow of SDE. So that, we are able to extend to the solution of similar SPDEs the decomposition based on the solutions of two SDEs and their inverses. The second part is concerned with forward utilities, consistent with a given incomplete financial market, that can be observed but given exogenously to the investor. As in \cite{zar-03}, market dynamics are considered in an equilibrium state, so that the investor becomes indifferent to any action she can take in such a market. After having made explicit the constraints induced on the local characteristics of consistent utility and its conjugate, we focus on the marginal utility SPDE by showing that it belongs to the previous family of SPDEs. The associated two SDE's are related to the optimal wealth and the optimal state price density, given a pathwise explicit representation of the marginal utility. This new approach addresses several issues with a new perspective: dynamic programming principle, risk tolerance properties, inverse problems. Some examples and applications are given in the last section

Ramsey Rule with Progressive utility and Long Term Affine Yields Curves

The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial, justifying the use of progressive utility. This paper studies, in a framework with affine factors, the yield curve given from the Ramsey rule. It first characterizes consistent progressive utility of investment and consumption, given the optimal wealth and consumption processes. A special attention is paid to utilities associated with linear optimal processes with respect to their initial conditions, which is for example the case of power progressive utilities. Those utilities are the basis point to construct other progressive utilities generating non linear optimal processes but leading yet to still tractable computations. This is of particular interest to study the impact of initial wealth on yield curves.Comment: arXiv admin note: substantial text overlap with arXiv:1404.189

Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling

The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial. Thus, after recalling some important properties on progressive utility, this paper first provides an extension of the notion of a consistent progressive utility to a consistent pair of progressive utilities of investment and consumption. An optimality condition is that the utility from the wealth satisfies a second order SPDE of HJB type involving the Fenchel-Legendre transform of the utility from consumption. This SPDE is solved in order to give a full characterization of this class of consistent progressive pair of utilities. An application of this results is to revisit the classical backward optimization problem in the light of progressive utility theory, emphasizing intertemporal-consistency issue. Then we study the dynamics of the marginal utility yield curve, and give example with backward and progressive power utilities

An Exact Connection between two Solvable SDEs and a Nonlinear Utility Stochastic PDE

Motivated by the work of Musiela and Zariphopoulou \cite{zar-03}, we study the Itô random fields which are utility functions $U(t,x)$ for any $(\omega,t)$. The main tool is the marginal utility $U_x(t,x)$ and its inverse expressed as the opposite of the derivative of the Fenchel conjuguate \tU(t,y). Under regularity assumptions, we associate a $SDE(\mu, \sigma)$ and its adjoint SPDE$(\mu, \sigma)$ in divergence form whose $U_x(t,x)$ and its inverse -\tU_y(t,y) are monotonic solutions. More generally, special attention is paid to rigorous justification of the dynamics of inverse flow of SDE. So that, we are able to extend to the solution of similar SPDEs the decomposition based on the solutions of two SDEs and their inverses. The second part is concerned with forward utilities, consistent with a given incomplete financial market, that can be observed but given exogenously to the investor. As in \cite{zar-03}, market dynamics are considered in an equilibrium state, so that the investor becomes indifferent to any action she can take in such a market. After having made explicit the constraints induced on the local characteristics of consistent utility and its conjugate, we focus on the marginal utility SPDE by showing that it belongs to the previous family of SPDEs. The associated two SDE's are related to the optimal wealth and the optimal state price density, given a pathwise explicit representation of the marginal utility. This new approach addresses several issues with a new perspective: dynamic programming principle, risk tolerance properties, inverse problems. Some examples and applications are given in the last section

2-Phenyl­anilinium dihydrogen phosphate

In the crystal structure of the title compound, C12H12N+·H2PO4 −, the dihydrogen phosphate anions and the 2-phenyl­anilinium cations are associated via O—H⋯O and N—H⋯O hydrogen bonds so as to build inorganic layers around the x = 1/2 plane. The organic entities are anchored between these layers through C—H⋯O hydrogen bonds, forming a three-dimensional infinite network. The dihedral angle between the aromatic rings is 44.7 (4)°

Endovascular management of an isolated common iliac artery aneurysm: a case report

Isolated iliac artery aneurysms are rare, and treatment by conventional surgery gives good results. Endovascular repair of such aneurysms has recently become the preferred form of treatment, provided the appropriate anatomy for endovascular repair exists. We report the case of a 60-year-old man admitted in our department for an aneurysm of the left primitive iliac artery revealed by intermittent claudication and treated by a covered stent after embolization of the hypogastric artery by an Amplatzer Vascular Plug with a good result. This case highlights the importance of preservation of the collaterals of the hypogastric artery when you treat such entity; in order to avoid transient gluteal claudication and sexual dysfunction

Synthesis and physico-chemical studies of a novel bis [3,5-diamino-4H-1,2,4-triazol-1-ium] dichloride monohydrate

The title new compound, (C2H6N5+)2, 2Cl−.H2O, contains two 3,5-diamino-4H-1,2,4-triazol-1-ium cations, two chloride anions and one water molecule. The crystal structure is stabilized by O - H···Cl, N - H···Cl, N - H···O and N - H···N hydrogen bonds, one of them being a three-center interaction. Strong π - π stacking interactions between neighboring triazolium rings are present, with a centroid - centroid distance of 3.338 (7) Å. The exocyclic N atoms are sp2 hybridized, as evidenced by bond lengths and angles, in agreement with an enamine-imine tautomerism. A dielectric spectroscopic study of the title compound was performed. The 13C CP-MAS NMR spectrum is in agreement with crystallographic data. The infrared spectrum has been recorded at ambient temperature and interpreted on the basis of literature data. The temperature dependence of the imaginary part of the permittivity constant was analyzed with the Cole - Cole formalism in the temperature range 325 - 375 K

2,6-Dimethyl­anilinium chloride monohydrate

In the title hydrated mol­ecular salt, C8H12N+·Cl−·H2O, the component species inter­act by way of N—H⋯O, N—H⋯Cl and O—H⋯Cl hydrogen bonds, resulting in a three-dimensional network

4-Acetamido­anilinium nitrate monohydrate

In the title hydrated salt, C8H11N2O+·NO3 −·H2O, the N—C bond distances [1.349 (2) and 1.413 (2) Å] along with the sum of the angles (359.88°) around the acetamide N atom clearly indicate that the heteroatom has an sp 2 character. The ammonium group is involved in a total of three N—H⋯O hydrogen bonds, two of these are with a water mol­ecule, which forms two O—H⋯O hydrogen bonds. All these hydrogen bonds link the ionic units and the water mol­ecule into infinite planar layers parallel to (100). The remaining two N—H⋯O inter­actions in which the ammoniun group is involved link these layers into an infinite three-dimensional network